2 years ago

Aaah! new group for trigonometry :)
Let me start this by asking to expand sin 5x in powers of sin x.
Only for those who have started learning trigonometry and never tried this.
Those who already know how to, can give other methods, not discussed here, later.

Noting that sin(5x)= Im(cos(5x)+isin(5x))=Im(e^(5ix))=Im((e^ix)^5)
=Im((cos(x)+isin(x))^5). So basically, if you see what the imaginary part of:\[(\cos(x)+i \sin(x))^5\]is, you will have a formula for sin(5x).